For me something very different helped:
I logged out => This made the ‘install UE5’ button available again. So I clicked it, and it was adding it to my Library, then in the library it asked me to sign in again.
worked from there
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this is def the solution!! ok… i had this same problem, no download ue anywhere or be4 that just an older version, i uninstalled epic launcher twice and no succes. but the third time I thought to go to settings/apps and delete both epic launcher and epic online services. went to unreal site to be sure i got the right updated version of epic launcher, and boom after install and logging in, there was ue5 as a choice. 
also first i had the option to download older version only after i deleted that by accident my button stayed greyed out and was unable to press plus or get any unreal engine
But for me, it can install, but it only says “Please Wait…”.
I thought it was normal, but after waiting for more than 1 minute or maybe 3 minutes more, it’s the same and it just says something like that and won’t install.
Even though I’ve also tried repeatedly and I’ve changed the wi-fi or internet data many times, but the result is the same… :((((
Guys, I solved this
Just simply stop or cancel all other downloading installers, UE Install button will work
Thank you : )
This worked for me. Didn’t have to install Twinmotion, cancelled when choosing a file path and it was enough to reactivate the +. Thanks!